Among other things, an apparatus comprises quantum units; and couplers among the quantum units. Each coupler is configured to couple a pair of quantum units according to a quantum Hamiltonian characterizing the quantum units and the couplers. The quantum Hamiltonian includes quantum annealer Hamiltonian and a quantum governor Hamiltonian. The quantum annealer Hamiltonian includes information bearing degrees of freedom. The quantum governor Hamiltonian includes non-information bearing degrees of freedom that are engineered to steer the dissipative dynamics of information bearing degrees of freedom.